First of all, you are not alone. The way godhood and magic works in the Malazan books is very confusing. I like to think that it's intentionally that way: what we're reading is merely the confused understanding that a few mortals have about something that is fundamentally incomprehensible.
However, it is not true that the only way to be a god was to control a Warren. There were many ways for a being in this universe to have god-like powers. As the author himself explains:
are all gods ascendants? If you mean ascendant in the general sense of being very powerful, then yes. If you mean ascendant in terms of progression, then there are exceptions. Most of the animistic ones, for example (the totemic, tribal ones) derived from the act of worship, or the attribution of significance to a particular place. - Q and A with malazanempire No 2 (2003) src
Thus, it seems like there are at least three ways to become a god in the Malazan universe:
The Elder Gods
The "elder" gods are the gods who have always been gods. These are creatures like Kilmandaros of the Forkrul Assail, and Mother Dark of the Tiste Andii. They were physical beings, capable of (for example) having children, but they also represented fundamental forces of the universe. In particular, the warrens themselves were the "veins" of K'rul, one of the elder gods.
These gods mostly seem to have disappeared from the world by the time of the story, though not entirely.
The "Totemic" Gods
Throughout the series, we occasionally run into gods that seem to exist merely because they represent something that a lot of people worship. Fener, in your question, is an example of this. He's the God of War, and exists because there are a whole lot of people who worship war. As long as that continues to be the case, there will always be a God of War.
The identity of these gods appears to change as needed; for example, during the story we see Fener, who's worship has fallen off, replaced by a new God of War.
These are otherwise-mortal beings who have managed to somehow cheat death. Not all Ascendants are gods, but they have the potential to be. Seizing control of a warren appears to be the primary means of doing this, but not the only one. This, for example, is how Shadowthrone becomes a god -- he took over an abandoned warren.
But it's not really the warren, but rather the idea of "being worshipped", that separates an Ascendant God from just a regular Ascendant. I believe that most Ascendants we see in the series never really achieve god-hood. Those that control a particular warren have a staked a claim on some aspect of the world that will grant them followers, but there are other ways to become worshipped. The replacement God of War, for example, is an initally-human Ascendant. Oponn appears to have achieved god-hood simply by nature of being the grandchildren of an Elder God, and having control over some aspect of the world that draws people to worship them.
The Warrens and The Paths
Also, since you asked, the warrens are very closely tied to the idea of godhood, but they're much more closely tied to the idea of magic.
The warrens, conceptually, are the "veins" of the god K'rul, which he has opened to mortals to allow them to use magic. But the warrens are also a physical place -- you can travel through them, and even live in them. For example, the Tiste Andii race spent their early existence living inside of their warren, until it was damaged and they were forced out.
There are two different kinds of warrens that appear in the series:
Elder warrens are the primordial warrens, ones closely associated with the Elder Races and the Elder Gods. Typically, these Warrens are open only to those of a particular race; for example, Anomander Rake is both a Tiste Andii and a Soultaken, so he can use Starvald Damelain (the Dragon Warren) and Kurald Galain (the Tiste Andii warren).
The Paths are the warrens open to human mages; these seem to pop into existence as needed. They are called the Paths because human mages with access to a warren can use it to travel long distances in short time periods. In addition, different humans have access to different warrens, usually only one at a time. (Quick Ben has access to many, but he's super special.)
It might seem unfair, that humans have access to a whole range of warrens while the Elder Races only have one each, but the Elder Warrens are tapping directly into the primal magic of the universe. Each one of them is orders of magnitude more powerful than any human warren. We see spells from, e.g. the Jaghut, using their warren, that dwarfs anything the most powerful human mages could match.
Probably the best way to think of it is that the one "human racial" warren is split up into smaller, more specialized "sub-warrens", so most humans only have access to a tiny fraction of its power. (This isn't something that's ever stated in the books, I just made it up, but IMO it's the best way to keep the relative strength of the warrens in mind.)